On the new extension of distance-balanced graphs
In this paper, we initially introduce the concept of $n$-distance-balanced property which is considered as the generalized concept of distance-balanced property. In our consideration, we also define the new concept locally regularity in order to find a connection between $n$-distance-balanced...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Isfahan
2016-12-01
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| Series: | Transactions on Combinatorics |
| Subjects: | |
| Online Access: | http://toc.ui.ac.ir/article_15048_3968109258ac5aaddf5a16c03fc677d5.pdf |
| Summary: | In this paper, we initially introduce the concept of $n$-distance-balanced property which is considered as the generalized concept of distance-balanced property. In our consideration, we also define the new concept locally regularity in order to find a connection between $n$-distance-balanced graphs and their lexicographic product. Furthermore, we include a characteristic method which is practicable and can be used to classify all graphs with $i$-distance-balanced properties for $ i=2,3 $ which is also relevant to the concept of total distance. Moreover, we conclude a connection between distance-balanced and 2-distance-balanced graphs. |
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| ISSN: | 2251-8657 2251-8665 |